Truth Tables

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Show your work for each problem.

1.
How many rows does a truth table with 3 variables have?
1. a)9
2. b)3
3. c)8
4. d)6
2.
How many rows does a truth table for $P$ and $Q$ need?
3.
Set up the variable columns of a truth table for $P$ , $Q$ and $R$ in the standard order.
4.
In the standard order of an 8-row truth table, which pattern does the last column $R$ have?
1. a)F, F, F, F, T, T, T, T
2. b)T, T, F, F, T, T, F, F
3. c)T, F, T, F, T, F, T, F
4. d)T, T, T, T, F, F, F, F
5.
A truth table has 64 rows. How many variables does the expression have?
6.
Build the truth table for $\neg P \land Q$ . In which row is it true? Use the standard row order (row 1 is $P$ = T, $Q$ = T).
7.
In how many of the 4 rows of the truth table is $\neg P \lor Q$ true?
8.
Which expression is a tautology?
1. a) $P \land Q$
2. b) $P \lor \neg P$
3. c) $\neg P \lor Q$
4. d) $P \land \neg P$
9.
In how many of the 8 rows is $P \land (Q \lor R)$ true?
10.
In how many of the 8 rows of the truth table is $P \lor (Q \land R)$ true?
11.
Use a truth table to check whether $(P \lor Q) \lor \neg Q$ is a tautology.
12.
Which expression is logically equivalent to $\neg(P \lor Q)$ ?
1. a) $P \land Q$
2. b) $\neg P \lor \neg Q$
3. c) $\neg P \land \neg Q$
4. d) $\neg P \lor Q$
13.
Use a truth table to check whether $(P \land Q) \land \neg P$ is a contradiction. Use the standard row order (row 1 is $P$ = T, $Q$ = T).
14.
What does the truth table of $(P \lor Q) \land \neg P$ show?
1. a)It is a contradiction
2. b)It is equivalent to $P$
3. c)It is neither: true in exactly 1 row
4. d)It is a tautology
15.
In how many of the 4 rows is $(P \land \neg Q) \lor (\neg P \land Q)$ true?
16.
Use a truth table to check whether $P \land (Q \lor R)$ and $(P \land Q) \lor (P \land R)$ are equivalent.
17.
A student claims that $\neg(P \land Q)$ is equivalent to $\neg P \land \neg Q$ . Check it with a truth table. Use the standard row order (row 1 is $P$ = T, $Q$ = T).
18.
Build the truth table for $\neg P \lor (Q \land \neg R)$ . In how many of the 8 rows is it true?